Effect of coastal boundary resolution and mixing upon internal wave generation and propagation in coastal regions

A non-linear two-dimensional vertically stratified cross-sectional model of a constant depth basin without rotation is used to investigate the influence of vertical and horizontal diffusion upon the wind-driven circulation in the basin and the associated temperature field. The influence of horizontal grid resolution, in particular the application of an irregular grid with high resolution in the coastal boundary layer is examined. The calculations show that the initial response to a wind impulse is downwelling at the downwind end of the basin with upwelling and convective mixing at the opposite end. Results from a two-layer analytical model show that the initial response is the excitation of an infinite number of internal seiche modes in order to represent the initial response which is confined to a narrow near coastal region. As time progresses, at the downwind end of the basin a density front propagates away from the boundary, with the intensity of its horizontal gradient and associated vertical velocity determined by both horizontal and vertical viscosity values. Calculations demonstrate the importance of high horizontal grid resolution in resolving this density gradient together with an accurate density advection scheme. The application of an irregular grid in the horizontal with high grid resolution in the nearshore region enables the initial response to be accurately reproduced although physically unrealistic short waves appear as the frontal region propagates onto the coarser grid. Parameterization of horizontal viscosity using a Smagorinsky-type formulation acts as a selective grid size-dependent filter, and removes the short-wave problem although enhanced smoothing can occur if the scaling coefficient in the formulation is too large. Calculations clearly show the advantages of using an irregular grid but also the importance of using a grid size-dependent filter to avoid numerical problems.     

Array measurements of the bottom boundary layer and the internal wave field on the continental slope

Abstract

An array of current meters was placed on the continental slope and rise for two months in the autumn of 1970. The bottom boundary layer was penetrated on the slope. On the smallest array scale, of the order of 1 kilometer, the array functioned as a directional internal wave antenna. Moving shoreward, the current spectra show strong suppression of the inertial peak and strong enhancement of the semidiurnal tide. The measured wave number spectra show that the tidal energy is almost completely baroclinic, and probably being generated in the region where the slope becomes “critical” for the tidal period. If this area is typical of worldwide conditions, a substantial fraction of the dissipation of surface tides takes place on the continental slopes by conversion to baroclinic waves. The bottom boundary layer has been modeled by an extension of the work of Ellison (1956) to a sloping boundary in a fluid of positive stability. An equivalent constant eddy coefficient has the value 3 cm²/sec as determined from the measurements.     

Influence of bottom frictional effects in sill regions upon lee wave generation and implications for internal mixing

A cross-sectional nonhydrostatic model using idealized sill topography is used to examine the influence of bottom friction upon unsteady lee wave generation and flow in the region of a sill. The implications of changes in shear and lee wave intensity in terms of local mixing are also considered. Motion is induced by a barotropic tidal flow which produces a hydraulic transition, associated with which are convective overturning cells, wave breaking, and unsteady lee waves that give rise to mixing on the lee side of the sill. Calculations show that, as bottom friction is increased, current profiles on the shallow sill crest develop a highly sheared bottom boundary layer. This enhanced current shear changes the downwelling of isotherms downstream of the sill with an associated increase in the hydraulic transition, wave breaking, and convective mixing in the upper part of the water column. Both short and longer time calculations with wide and narrow sills for a number of sill depths and buoyancy frequencies confirm that increasing bottom friction modifies the flow and unsteady lee wave distribution on the downstream side of a sill. Associated with this increase in bottom friction coefficient, there is increased mixing in the upper part of the water column with an associated decrease in the vertical temperature gradient. However, this increase in mixing and decrease in temperature gradient in the upper part of the water column is very different from the conventional change in near-bed temperature gradient produced by increased bottom mixing that occurs in shallow sea regions as the bottom drag coefficient is increased.     

Turbulence in the presence of internal waves in the bottom boundary layer of the California inner shelf

Turbulence measurements were collected in the bottom boundary layer of the California inner shelf near Point Sal, CA, for 2 months during summer 2015. The water column at Point Sal is stratified by temperature, and internal bores propagate through the region regularly. We collected velocity, temperature, and turbulence data on the inner shelf at a 30-m deep site. We estimated the turbulent shear production (P), turbulent dissipation rate (ε), and vertical diffusive transport (T), to investigate the near-bed local turbulent kinetic energy (TKE) budget. We observed that the local TKE budget showed an approximate balance (P?≈?ε) during the observational period, and that buoyancy generally did not affect the TKE balance. On a finer resolution timescale, we explored the balance between dissipation and models for production and observed that internal waves did not affect the balance in TKE at this depth.     

Numerical study on wave propagation over a fluid-mud layer with different bottom conditions

Wave decay over a muddy seabed has been widely reported. In previous studies, the fluid-mud layer is usually treated as a homogeneous layer with a certain thickness lying on the rigid bottom. However, the muddy seabed beneath a fluid-mud layer is usually movable in practice. This study aims to find out the influence of the movable seabed beneath a fluid-mud layer. For this purpose, a numerical model for wave propagation over a multilayered muddy seabed is developed, in which water is treated as a Newtonian fluid, and the rheology of mud is described by a visco-elastic–plastic model. The laboratory experiments of Sakakiyama and Bijker (J Waterw Port Coast Ocean Eng 115(5):614–633, 1989) are chosen to validate the numerical model. The model is then employed to investigate the movement of a fluid-mud layer with different conditions of the underlying mud layer and its influence on wave decay. It is found that the underlying mud layer plays a very important role in the wave–mud interaction and greatly affects the wave decay rate.     

A numerical model of the wave boundary layer

A numerical model of deep, uniform, oscillatory, rough-turbulent boundary-layer flow is described. The model is based upon the governing horizontal momentum equation and a closure scheme involving the turbulent-energy equation and various turbulence-scaling laws. Finite difference solutions of these equations are obtained for a range of values of the ‘relative roughness’ (A₀/k_s), whereA₀ is the excursion amplitude of the water particles in the free-stream flow andk_s is the ‘equivalent bed roughness’. Typical vertical profiles of horizontal velocity, turbulence energy and eddy viscosity, and time-series of the bed shear stress are presented. The model results are then used to determine the wave drag coefficient, boundary-layer thickness and phase lead of the bed shear stress over the free-stream velocity, each as a function ofA₀/k_s. These results are shown to be in generally good agreement with previous experimental and theoretical results. Finally, the model is used to test for the existence of a universal velocity distribution for uniform oscillatory (sinusoidal) rough-turbulent flow. The ‘law of the wall’ and the ‘defect law’ proposed by Jonsson (1980, Ocean Engineering, 7, 109–152) are well supported by the model, and the existence of a logarithmic ‘velocity overlap layer’ in which both of these laws are valid is demonstrated forA_o/k_s30.     

Ceilometer observations of the boundary layer over Warsaw,Poland

Jenoptik’s CHM 15k ceilometer was used to monitor the vertical structure of the atmospheric boundary layer (ABL) over Warsaw, from 2008 until 2011, on Mondays and Thursdays, in 24h periods. Hereby, we present an assessment of the signal-to-noise ratio along with a sensitivity study of signal smoothing methods developed in-house. With the proposed averaging, ceilometer attenuated-backscatter signals reached the high troposphere, which makes this sensor competitive to a single-wavelength elastic lidar. The smoothed signals were employed as an input for algorithms developed to automatically detect the ABL height, clouds, fog, and precipitation in the lower troposphere. The classification of weather conditions was validated by the METAR reports from the Warsaw Airport. The obtained ABL heights were compared to those assessed from radio-soundings from a nearby meteorological station WMO12374 in Legionowo. An inter-comparison of the ABL heights, derived by using the Jenoptik’s automated routine against the in-house developed algorithms, is in favor of the latter. The presented four annual cycles of the ABL height, obtained with various derivative-based methods, are the first such long-term results reported using the CHM 15k sensor in Eastern Europe.     

含流体层的河谷场地对地震波散射的间接边界元法模拟

结合单相介质动力格林函数和流体域格林函数,将间接边界元方法拓展到含流体层河谷对地震波散射的求解,并结合具体算例进行大量参数分析。研究结果表明,含流体层河谷地形对平面P波、SV波入射时的地震响应受控于入射波频率、入射波角度及流体深度等多种因素。总体来看:① 在低频域内,含流体河谷底部及附近地表的频谱特性与不含流体的河谷反应基本一致;② P波入射时在水层体系共振频率处,河谷底部位移缩小效应显著,而此频率处流体表面位移达到最大;③ 流体层具有吸收地震波能量的作用,流体深度越大,河谷表面及附近地表的地震动位移越小。研究成果可在一定程度上为河谷地形附近地震动效应的评估及防震减灾工作提供理论依据。      

Numerical modeling of the atmospheric boundary layer over a hilly landscape

Summary A model for calculating the wind, turbulent exchange coefficients and a modification of the initial temperature over a hilly terrain is described. The paper mainly deals with a numerical realization of the model equations. Some features of the splitting method are discussed in detail. A special version of the splitting method suitable for solving the atmospheric boundary layer is described.

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On steady and travelling waves over bottom topography in the model of homogeneous flow in a beta-plane channel

Abstract

A spectral low-order model is proposed in order to investigate some effects of bottom corrugation on the dynamics of forced and free Rossby waves. The analysis of the interaction between the waves and the topographic modes in the linear version of the model shows that the natural frequencies lie between the corresponding Rossby wave frequencies for a flat bottom and those applying in the “topographic limit” when the beta-effect is zero. There is a possibility of standing or eastward-travelling free waves when the integrated topograhic effect exceeds the planetary beta-effect.

The nonlinear interactions between forced waves in the presence of topography and the beta-effect give rise to a steady dynamical mode correlated to the topographic mode. The periodic solution that includes this steady wave is stable when the forcing field moves to the West with relatively large phase speed. The energy of this solution may be transferred to the steady zonal shear flow if the spatial scale of this zonal mode exceeds the scale of the directly forced large-scale dynamical mode.     

夏季青藏高原地区近地层水汽进入平流层的特征分析

青藏高原为亚洲季风区的典型代表区域,研究其水汽进入平流层的过程和机理对认识全球气候和大气环境变化具有一定的现实意义. 本文基于中尺度气象模式(WRF)的模拟输出结果(2006年8月20日至8月26)驱动拉格朗日大气输送模式FLEXPART,通过追踪并解析气块的三维轨迹以及温度、湿度等相关物理量的相关变化特征,初步分析了夏季青藏高原地区近地层-对流层-平流层的水汽输送特征. 研究结果表明,源于高原地区近地层的水汽在进入平流层的过程中受南亚高压影响下的大尺度环流和中小尺度对流的共同影响.首先,在对流抬升作用下,气块在短时间内(24 h)可抬升到9~12 km的高度,然后在南亚高压闭合环流影响下,相当部分气块在反气旋的东南侧穿越对流层顶进入平流层中,并继续向低纬热带平流层输送,进而参与全球对流层-平流层的水汽循环过程. 在对流抬升高度上气块位置位于高原的西北侧,然而气块拉格朗日温度最小值主要分布于高原南侧,两个位置上气块的平均位温差值可达15~35 K,这种显著的温度差异将导致气块进入平流层时"脱水". 比较而言,夏季青藏高原地区近地层水汽进入平流层的多寡主要和大尺度汽流的垂直输送有关,而深对流的作用相对较弱.     

Oblique surface wave propagation over a small undulation on the bottom of an ocean

The problem of oblique water wave diffraction by small undulation of the bottom of a laterally unbounded ocean is considered using linear water wave theory. A perturbation analysis is employed to obtain the velocity potential, the reflection and the transmission coefficients up to the first order in terms of integrals involving the shape functions c(x) representing the bottom undulation. Finite cosine transform is used to find the first order potential, and this potential is utilised in obtaining the first order reflection and transmission coefficients. Some particular forms of the shape function representing an exponentially damped undulation, a single hump and a patch of sinusoidal ripples are considered and the integrals for the reflection and transmission coefficients are evaluated. For the exponentially damped undulation, it is observed that the reflection ceases much before transmission while for the single hump, reflection and transmission go hand in hand up to a certain value of the wavenumber, after which they vanish. For the patch of sinusoidal ripples having the same wavenumber, the reflection coefficient up to the first order is found to be an oscillatory function in the quotient of twice the component of the wavenumber along x-axis and the ripple wavenumber. When this quotient becomes one, the theory predicts a resonant interaction between the bed and free surface, and the reflection coefficient becomes a multiple of the number of ripples. High reflection of the incident wave energy occurs if this number is large. Also, when a patch of ripples having different wavenumbers is considered the same result follows. Known results for the normal incidence are recovered as special cases for the patch of sinusoidal ripples. The theoretical observations are shown computationally.     

The effect of bottom topography on the Agulhas Current

Summary Methods used by Warren and later modified by Niiller and Robinson have been used to investigate the Agulhas Current and other currents associated with it. The results show that with the assistance of a small bottom current of 4 cm/s in the same direction as the main current, the Agulhas Current can proceed round the Cape of Good Hope during three out of four seasons of the year. During the northern winter season, however, the Agulhas Current is so strong that the bottom current may not be able to be so effective and then the Current doubles back near the Agulhas Plateau to form an Agulhas Return Current. There is, however, all the year round an eastward current flowing south of the Agulhas Current but except during the northern winter season, this fed mainly from outside the Agulhas Current area. With a small bottom current of about 2 cms/ the current gets deflected round the Agulhas Plateau to give a meandering effect.     

海底边界层异常(地震海洋学)反射地震特征的地球物理分析

通过对南海北部与西部大量反射地震剖面海水层部分进行再处理,与以往地震海洋学主要关注海水层内部的反射结构不同,本文重点对海底附近水体的各种复杂反射地震特征进行分类、分析与总结.与传统对海底边界层的定义不同,我们将海底边界附近的水体称之为海底边界层.本文利用传统地震相分析方法,分析海底边界层各种复杂反射地震结构的几何形态、内部反射结构、连续性、振幅以及视频率特征,结合过去相关的地震海洋学研究成果、海底边界层理论与其它各种海底附近作用/过程,不仅对中尺度涡旋、内孤立波和背风波在地震剖面上的反射地震特征进行了归类与分析,并推断最新发现的一些反射地震特征可能揭示的各种海洋作用/过程,例如不同的地震相特征可能反映了海底湍流边界层,海底沉积物再悬浮,天然气渗漏羽状流和麻坑内部异常上升流相关海底界面作用过程.结果分析表明,地震海洋学方法不仅能够对海洋内波、涡旋等物理海洋现象进行研究,同时也能够对海底附近各种复杂海洋作用/过程进行成像,从而拓展了地震海洋学的研究领域,一定程度上也能为过去不能有效对海底边界面发生的各种冷泉热液活动、生物和沉积等作用过程进行现场观测提供新的探测方法和研究视角.     

Perfectly matched layer boundary conditions for frequency-domain acoustic wave simulation in the mesh-free discretization

Mesh-free discretization, flexibly distributing nodes without computationally expensive meshing process, is able to deal with staircase problem, oversampling and undersampling problems and saves plenty of nodes through distributing nodes suitably with respect to irregular boundaries and model parameters. However, the time-domain mesh-free discretization usually exhibits poorer stability than that in regular grid discretization. In order to reach unconditional stability and easy implementation in parallel computing, we develop the frequency-domain finite-difference method in a mesh-free discretization, incorporated with two perfectly matched layer boundary conditions. Furthermore, to maintain the flexibility of mesh-free discretization, the nodes are still irregularly distributed in the absorbing zone, which complicates the situation of artificial boundary reflections. In this paper, we implement frequency-domain acoustic wave modelling in a mesh-free system. First, we present the perfectly matched layer boundary condition to suppress spurious reflections. Moreover, we develop the complex frequency shifted–perfectly matched layer boundary condition to improve the attenuation of grazing waves. In addition, we employ the radial-basis-function-generated finite difference method in the mesh-free discretization to calculate spatial derivatives. The numerical experiment on a rectangle homogeneous model shows the effectiveness of the perfectly matched layer boundary condition and the complex frequency shifted–perfectly matched layer boundary condition, and the latter one is better than the former one when absorbing large angle incident waves. The experiment on the Marmousi model suggests that the complex frequency shifted–perfectly matched layer boundary condition works well for complicated models.     

A Raman lidar to measure water vapor in the atmospheric boundary layer

A new multi-telescope scanning Raman lidar designed to measure the water vapor mixing ratio in the atmospheric boundary layer for a complete diurnal cycle with high resolution spatial (1.25 m) and temporal (1 s) resolutions is presented. The high resolution allows detailed measurements of the lower atmosphere and offers new opportunities for evaporation and boundary layer research, atmospheric profiling and visualization. This lidar utilizes a multi-telescope design that provides for an operational range with a nearly constant signal-to-noise ratio, which allows for statistical investigations of atmospheric turbulence. This new generation ground-based water vapor Raman lidar is described, and first observations from the Turbulent Atmospheric Boundary Layer Experiment (TABLE) are presented. Direct comparison with in-situ point measurements obtained during the field campaign demonstrate the ability of the lidar to reliably measure the water vapor mixing ratio. Horizontal measurements taken with time are used to determine the geometric characteristics of coherent structures. Vertical scans are used to visualize nocturnal jet features, layered structures within a stably stratified atmosphere and the internal boundary layer structure over a lake.     

Effect of soil water-repellent layer depth on post-wildfire hydrological processes

Soil water repellency induced by wildfires can alter hydraulic properties and hydrologic processes; however, the persistence and vertical position (i.e., depth) of water-repellent layers can vary between systems and fires, with limited understanding of how those variations affect infiltration processes. This study occurred in two forested locations in the south-central Appalachian Mountains that experienced wildfires in late 2016: Mount Pleasant Wildfire Refuge, Virginia, and Chimney Rock State Park, North Carolina. In each location, sites were selected to represent unburned conditions and low to moderate burn intensities. At each site, we measured the soil water repellency at the surface (ash layer or O horizon) and ~2 cm below the surface (A horizon) using the water drop penetration time method (n = 10–14). Soil water content was also measured over the upper 10 cm of the soil (n = 10), and infiltration tests were conducted using a tension infiltrometer (n = 6–8). The results showed that soil repellency was highest in the surface layer at the Mount Pleasant location and was highest in the subsurface layer at the Chimney Rock location. Soil water content was lower in unburned soil than in burned soil, especially for measurements taken immediately postfire, with soil water content negatively correlated with water repellency. Water repellency in the surface layer significantly reduced relative infiltration rates (estimated as differences between initial and steady-state rates), whereas subsurface water repellency did not affect relative infiltration. As a result, water repellency persisted longer in sites with surface as opposed to subsurface water repellency. Finally, differences between burned and unburned sites showed that although the wildfires increased the occurrence of water repellency, they did not alter the underlying relationship between relative infiltration and water repellency of the surface soil.